Modeling the effect of debonding on the constitutive response of heterogeneous materials

Experimental studies have observed that particulate composite systems experience damage in three principal modes: failure of the interface between particle and binder; tearing of the matrix; and fracture of the particle. Interfacial debonding is often a precursor to the other failure processes and plays a key role in the constitutive response of solid propellant, a compliant elastomeric matrix containing a high volume fraction of stiff particles. These particles range from a few micrometers to several hundred micrometers in diameter. Since solid propellant structures are on the scale of meters, a multiscale method is necessary to accurately simulate damage and failure.;This work has focused on using two homogenization approaches to investigate the relationship between microstructural damage and macroscopic constitutive response: a nonlinear finite element solution incorporating the Mathematical Theory of Homogenization (MTH) and a micromechanics model based on Mori-Tanaka homogenization. The rigorous mathematical framework of MTH couples the macroscale and the microscale through asymptotic analysis. MTH-based finite element simulations, performed on a periodic unit cell, capture details of particle interactions, local stress concentrations and asymmetries in the microstructural processes. Comparatively inexpensive micromechanics models, on the other hand, ignore many of these complexities but accurately reproduce important features of the constitutive response and provide additional insights into the physics of dewetting.;The two modeling approaches are compared for the axisymmetric case of circular particles debonding under equibiaxial loading. MTH simulations were used to provide a reference solution against which the micromechanics results could be evaluated. The comparison was made for small strain; a similar comparison performed using nonlinear kinematics found comparable results. The interaction between the two methods differentiates those features of the model which significantly impact the results from those which do not. It was demonstrated that for material systems with large differences between particle diameters, it is unnecessary to model the debonding of smaller particles; it is sufficient to represent their contribution to damage nucleation and to the stiffness of the matrix.;The small strain micromechanics approach is subsequently extended to consider the multiaxial response of composites containing elliptical particles. Unlike the axisymmetric case, the micromechanics model does not permit a purely analytic solution because both the loading and the geometry are two-dimensional. The interfacial traction field is therefore approximated by a Fourier series decomposition. The stresses and displacements are found using Muskhelishvili's method of complex potentials. The model was verified by comparison with the previously obtained results for circular inclusions. The macroscopic response is influenced by the particle size and aspect ratio as well as the applied loading condition. Refinement of the model is necessary in order to investigate the effect of loading direction.;Finally, the MTH-based finite element framework is used to evaluate the performance of periodic boundary conditions and minimal kinematic boundary conditions applied to the unit cell of a particulate composite material. Contrary to the predictions of some research, it is demonstrated that both boundary conditions capture localization even under inherently non-periodic loading.